RDPs are the subclass of Non-Markov Decision Processes where the dependency on the history of past events can be captured by a finite-state automaton. We consider a setting where the automaton that underlies the RDP is unknown, and a learner strives to learn a near-optimal policy using pre-collected data, in the form of non-Markov sequences of observations, without further exploration. We present RegORL, an algorithm that suitably combines automata learning techniques and state-of-the-art algorithms for offline RL in MDPs. RegORL has a modular design allowing one to use any off-the-shelf offline RL algorithm in MDPs. We report a non-asymptotic high-probability sample complexity bound for RegORL to yield an $\varepsilon$-optimal policy, which makes appear a notion of concentrability relevant for RDPs. Furthermore, we present a sample complexity lower bound for offline RL in RDPs. To our best knowledge, this is the first work presenting a provably efficient algorithm for offline learning in RDPs.

RDPs are the subclass of Non-Markov Decision Processes where the dependency on the history of past events can be captured by a finite-state automaton. We consider a setting where the automaton that underlies the RDP is unknown, and a learner strives to learn a near-optimal policy using pre-collected data, in the form of non-Markov sequences of observations, without further exploration. We present RegORL, an algorithm that suitably combines automata learning techniques and state-of-the-art algorithms for offline RL in MDPs. RegORL has a modular design allowing one to use any off-the-shelf offline RL algorithm in MDPs. We report a non-asymptotic high-probability sample complexity bound for RegORL to yield an \varepsilon -optimal policy, which makes appear a notion of concentrability relevant for RDPs.

Markov decision processes are typically used for sequential decision making under uncertainty. For many aspects however, ranging from constrained or safe specifications to various kinds of temporal (non-Markovian) dependencies in task and reward structures, extensions are needed. To that end, in recent years interest has grown into combinations of reinforcement learning and temporal logic, that is, combinations of flexible behavior learning methods with robust verification and guarantees. In this paper we describe an experimental investigation of the recently introduced regular decision processes that support both non-Markovian reward functions as well as transition functions. In particular, we provide a tool chain for regular decision processes, algorithmic extensions relating to online, incremental learning, an empirical evaluation of model-free and model-based solution algorithms, and applications in regular, but non-Markovian, grid worlds.

Regular Decision Processes (RDPs) are a recently introduced model that extends MDPs with non-Markovian dynamics and rewards. The non-Markovian behavior is restricted to depend on regular properties of the history. These can be specified using regular expressions or formulas in linear dynamic logic over finite traces. Fully specified RDPs can be solved by compiling them into an appropriate MDP. Learning RDPs from data is a challenging problem that has yet to be addressed, on which we focus in this paper. Our approach rests on a new representation for RDPs using Mealy Machines that emit a distribution and an expected reward for each state-action pair. Building on this representation, we combine automata learning techniques with history clustering to learn such a Mealy machine and solve it by adapting MCTS to it. We empirically evaluate this approach, demonstrating its feasibility.